@alpine sable Has your question been resolved?
#help-0
viscid hornet
I have no idea how to go about solving this. Thanks! It's question 3b
viscid hornet
How do you isolate the trig expression? I understand using the unit circle after.
ocean sealBOT
jan Niku (join us for @pomo)
remote heron
$4 \cos x = -2$
ocean sealBOT
jan Niku (join us for @pomo)
remote heron
$\cos x =- \frac 2 4$
ocean sealBOT
jan Niku (join us for @pomo)
remote heron
$\cos x = - \frac 1 2$
ocean sealBOT
jan Niku (join us for @pomo)
remote heron
where is x
alpine sable
lone heartBOT
alpine sable
anyone help
lone heartBOT
@alpine sable Has your question been resolved?
finite flax
anyone help
Hi, @alpine sable . Why don't you start by telling me where you are stuck?
alpine sable
I'm practicing for a quiz and need this question answered so I can compare it to the answers sheet.
https://gyazo.com/3f77e6947d5d172a7df392e7436d7647
I'm doing Simplify algebraic expressions.
vale wigeon
you realize that (a) this is an open-ended question and (b) we don't give out answers here, right?
alpine sable
Could you give instructions on how to do this specific one?
vale wigeon
write down an expression in r. it can be any expression you like, but keep in mind that it'll form an equation for you to solve, so act accordingly.
evaluate this expression at r=5.
then write down your expression, followed by the equals sign, followed by the value you got.
dapper bronze
lone heartBOT
dapper bronze
I dont get how 1/(y-1)^2 becomes
1/x-2
I thought u have to divide x-2 by (y-1)^2
How did numerator on the right side goes to numerator on the left side🥲
jagged imp
they took the reciprocal of each side/raised each side to the power of -1. An alternative way to look at is that they multiplied each side by (y-1)^2/(x-2).
jagged imp
.close if you dont wanna get randomly pinged by the bot in a few minues
unless you have more questions to ask
lone heartBOT
Available help channel!
jaunty silo
lone heartBOT
lone heartBOT
@jaunty silo Has your question been resolved?
carmine oar
how do i solve this
please start another channel
carmine oar
for a find the gradient/slope of l_1
lone heartBOT
@jaunty silo Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
sharp storm
I need help so badly. I have this Equation but i need to change it to get this one.
lone heartBOT
@sharp storm Has your question been resolved?
south sun
hi i require some help with this question where the recurrence relationship given in the solutions doesn't make sense I can't seem to make sense of it either
south sun
it's question e
this is the solution given in the scheme
But when i apply it, it works up to u2 for the first one but then fails immediately after for u3
As the n squared sequence goes 1, 4, 9, 16
marsh rapids
+2n+1, not +2u_n + 1
marsh rapids
if you look carefully at the formula, it is for u_(n+1), so for u_3 it is n=2
marsh rapids
the formula comes from the fact (n+1)² = n² + 2n + 1
south sun
Right but how would you realise this after being given just n squared as the sequence
marsh rapids
experience and practice. You recognise things
try to express the next term as a function of the previous term
south sun
Oh ok so its like now that ive seen this, next time i see un=n^2 I will know that its relationship is un + 2n + 1
marsh rapids
it's not about having seen everything, but when you do enough math you're able to see similarities
marsh rapids
you get an intuition for how to tackle problems
marsh rapids
always look at checks, then captures, then attacks. In math you also assimilate general rules that help guide you the right way
south sun
Man im dreading the maths im gnna have to learn for physics at uni
But things like this should make it easier
marsh rapids
like how would you find the recurrence relation for u_n = 2^(2^n) ?
south sun
Wtf is that abomination im currently trying to find one for n cubed to test if i understood this
marsh rapids
n^3 is the more logical continuation yes
marsh rapids
like how would you find the recurrence relation for u_n = 2^(2^n) ?
this is to apply that idea of expressing the next term as a function of the previous one(s) at a slightly higher level
but it's not a complicated formula
south sun
Just gimme a sec ill attempt that too after i can get this
marsh rapids
you can also do a general recurrence relation for n^k for any constant k when you've seen the binomial theorem
marsh rapids
,rotate 90
ocean sealBOT
marsh rapids
like how would you find the recurrence relation for u_n = 2^(2^n) ?
less than 5 short lines
marsh rapids
you can also do a general recurrence relation for n^k for any constant k when yo...
the binomial theorem is basically the theorem that gives you the formula for these coefficients, like 2 and 1 in 2n+1, or 3, 3, 1 in 3n²+3n+1
south sun
Ohhhh
Thats what it is
Funny cuz binomial is the next topic im doing after im finished with this
marsh rapids
The binomial theorem states that $$(a+b)^n = \sum_{k=0}^n \binom{n}{k} a^k b^{n-k}$$ where $$\binom{n}{k} = \frac{n!}{k! (n-k)!}$$ and are called binomial coefficients, which you will see a lot because of how often you put things to different powers, or that combinatorics get involved
ocean sealBOT
themateo713
south sun
Gimme sec bro the earlier question you gave is giving me a stroke trying to figure it out 😂
marsh rapids
it's not always because there is an answer in few lines that that answer is easy to reach
south sun
Ok so
For the un question
I noticed that when you put in the powers
You get this
marsh rapids
it's also not bad to know a few powers of 2 yes
marsh rapids
since they're all powers of 2, how about you just focus on the sequences of powers ? Setting u_n = 2^(v_n) and looking for that sequence v_n ? It should have a simpler formula
marsh rapids
though actually I'm not sure it helps to find the recurrence relation
it's a step in the right way, but it's a longer path at the end of the day
how would you express 2^8 as a function of 2^4 ? 2^16 as a function of 2^8 ?
marsh rapids
getting close
south sun
Ohhhh
Ok ok
I think i see it
Gimme a sec
Mannn
This is so sad
I feel like im on the border of getting it
But then i try something and it just doesnt work
Including un in the power just doesnt seem to work
marsh rapids
2^8 x 2^8 = 2^16
what's a*a for any a ?
marsh rapids
so since 2^8 = u3 and 2^16 = u^4, does that give you an idea ?
south sun
I git ut
It
I was thinking wrong
I had 2 as the base for the powers
And kept trying to make it work
The answer is just (un)^2
U1 = 4
marsh rapids
yes
south sun
What the hell man
marsh rapids
could you write a proof of that ?
south sun
This?
marsh rapids
like $u_{n+1} = (n+1)² = n²+2n+1 = u_n + 2n + 1$ but with this sequence
south sun
ocean sealBOT
themateo713
marsh rapids
a proof has at least as much generality as the property it seeks to prove
south sun
See the thing is i have no clue where you got (n+1)^2 from for that previous one i just applied the same thing to cubed to get the recurrence relationship
marsh rapids
as it turns out, a sequence of real numbers is just a function from N to R presented differently, emphasizing more the idea of succession than that of a graph or a mapping
so it's just plugging in values
south sun
Sorry what is the un for this one
Nvm found it
Yo
I did some working
And got this
Bottom right
marsh rapids
I'm not sure what's at the end (it's a bit too pixelated) but I don't think the last line is correct
marsh rapids
why a product all of a sudden
south sun
Cause i used the indices laws
marsh rapids
2^n still doesn't become 2n
south sun
I treated the 2 to the power 2 to the power n + 1
Yeah ur probablt right imma statt from the beginning
And make it a little more clear
Bro
Help
I feel like thats right but
I kind of have no clue where to go from here
As combining them back just brings me back to square 1
I got this
marsh rapids
like how would you find the recurrence relation for u_n = 2^(2^n) ?
I added the parentheses specifically to remove the ambiguity, so that you wouldn't read it as (2^2)^n = 4^n
south sun
marsh rapids
you also started from all but the start
south sun
Wait wdym all but the start
marsh rapids
meaning your starting point was wrong
marsh rapids
yes
south sun
Okkk
Just a quick question
I am supposed to apply indices laws right
And split up n and 1
marsh rapids
yes that's how you get started
south sun
Ok on it
marsh rapids
just don't turn the powers into products and you should be good
marsh rapids
turn the 2^n+1 into 2*2^n
south sun
Into product powers
marsh rapids
just not into 2*(n+1) like you did
south sun
Ohhhh
Yeah
Thats what i meant
I thought i wasnt supposed to do that
Quick question
2^n x 2 is NOT 4^n right
marsh rapids
no, because 4^n = (2^2)^n != 2^(n+1)
south sun
Yehp
Guessed as mucy
Im stuck
None of the indices laws im looking at are going to help me simplify this
marsh rapids
you already wrote the law that you should be using here on the previous page
marsh rapids
you reached the exit and kept going past it !
marsh rapids
you're supposed to recognize u_n at some point
south sun
Its just un squared
Wdymmm
Ok so
I only did 2 steps of working
One where i turned it into one power again with 2^(2^n)^2
Oh wait
Is that it
marsh rapids
that line (actually the equality on the left of that one) is precisely (u_n)²
south sun
Oh my god
Wtf 💀
The whole 2^2^n ia Un
OHHHH
OHHHH
Im so dense
Im so sorry 🗿
2^2 is 4
Which was u1
💀
So obviously the whole thing to the n is Un
Omggg
marsh rapids
$u_{n+1} = 2^{(2^{n+1})} = 2^{2*2^n} = (2^{(2^n)})² = u_n ^2$
ocean sealBOT
themateo713
marsh rapids
yes
marsh rapids
I suppose you're barely ever done proofs ?
marsh rapids
the idea with proofs is also to never forget where you're going
marsh rapids
which is also why a lot of questions are actually closed: as "show that ..." rather than "give a similar formula for ..." or "what about ...." or some other open question
astral jay
2^1024 is 179.769 uncentillion
marsh rapids
so I kindly made this one an open question
south sun
Ok thanks tho ill close this so others can make use of it
marsh rapids
don't need
south sun
Oh
marsh rapids
there are already open channels
south sun
Thats cool
marsh rapids
only close to say you're done and are going to leave, otherwise it's better to stay on the same channel
marsh rapids
resits ?
south sun
For pre uni exams
Doing them again basically
So i pass this time and get in
With the grades I need
And I have one month left till the finals start
marsh rapids
what's the curriculum ?
marsh rapids
isn't that the thing with a ton of stats ?
south sun
marsh rapids
for a general curriculum imo
south sun
yeah there is an entire section
for stats and mechanics
and this is only the year 2 stuff for pure maths
stats and mechanics have their own year 1 and year 2 b ooks
as u can see I was on 3.7
marsh rapids
how many hours a week is that ?
south sun
and i'm currently speedrunning through the book so even this break was a fair bit of time
im studying on my own now
the goal is 10 hours a day
so yeah ive spent a fair bit of time off topic today but its ok I learnt a thing or 2 about proofs
marsh rapids
the goal is 10 hours a day
good luck. But I meant at school how much do they study that curriculum in class ?
south sun
and got a key understanding thing done
ohhhh
uhhh
2 lessons a day avg
1 lesson being 50 mins
sooo
8 and a half hours
of in lesson learning per week
i think
marsh rapids
once again, basically every country putting the french math education to shame
marsh rapids
4h/week in 2nd year (it becomes optional, but they're going to reform the reform to fix that because the level is abyssmal), 6h/week in 3rd/last year, 9h/week if you took the optional "expert" math elective (I think that's the name ?)
south sun
yeah
its 9h per week here too for sixth form students
i know u have that weird ass ibacc system
we dont have that
after u finish gcses at 16
from 16 to 18 u have ur options
marsh rapids
the bac is just the diploma and you get tested on pretty much all subjects
south sun
and once u select those its 9hr per week per subject
u usually pick 3 options btw
4 if you're mental and don't like having rest time
marsh rapids
the bac is just the diploma and you get tested on pretty much all subjects
including french, english, philosophy, history/geography, sport, and your 2.5 specialities, as well as an oral exam on those
south sun
ah
well my time is running out as well now, i should really get back to covering content, thanks for your help today
marsh rapids
so during the last year the average scientific student has 6h math, 6h physics, 2h of "science" (really irrelevant), and that's it
south sun
ill get back to work though now so I hope you don't mind me closing channel.
south sun
so during the last year the average scientific student has 6h math, 6h physics, ...
ahhhh
makes sense but
seems too little
marsh rapids
it is
visual sonnet
i have this limit and should calculate it (if it exists) but isnt this just F -> (0,0) ?
visual sonnet
id just like an explanation if im right because im not sure i understand why, just remember ive seen a similar question
sorry i saw this question isnt allowed in this channel as its more advanced than pre uni math, ill move channel 😅
.close
lone heartBOT
lone heartBOT
Available help channel!
glad sluice
so we're trying to find the rank
lone heartBOT
so we're trying to find the rank
glad sluice
and after some row & column operations
how is it immediate?
that the first 3 rows/columns are linearly independent just from the column echelon form
and in general, if we get a echelon form for row/column, when can we say that the row/column vectors are linearly independent
and when they aren't
because every matrix has an echelon form but the row/column vectors aren't necessarily linearly independent
glad sluice
and in general, if we get a echelon form for row/column, when can we say that th...
but is this general argument true?
lone heartBOT
@glad sluice Has your question been resolved?
lone heartBOT
@glad sluice Has your question been resolved?
thick yoke
but is this general argument true?
The amount of leading coefficients is the amount of linearly independent vectors
at least
in the case above, because there are only 3 columns, and 3 leading coefficients, then the rank is 3
@glad sluice
glad sluice
The amount of leading coefficients is the amount of linearly independent vectors
so if a row/column is just 0 (in echelon form), that wont be counted in the number of linearly independent vectors?
sturdy notch
lone heartBOT
lone heartBOT
@sturdy notch Has your question been resolved?
lone heartBOT
@sturdy notch Has your question been resolved?
hard patio
ok, so do you know how angle 2 and angle 3 relate to each other?
lone heartBOT
@sturdy notch Has your question been resolved?
fresh relic
Can someone walk me through this?
lone heartBOT
sand smelt
.close
lone heartBOT
Available help channel!
lusty arrow
lone heartBOT
lusty arrow
Anyone know how to do part B?
tacit arch
do you know any numeric integration techniques?
lusty arrow
Trapezium rule
Never properly learnt it tho
@tacit arch do ylu@know how to do a I wanna make sure my answer is correct
tacit arch
lone heartBOT
@lusty arrow Has your question been resolved?
hardy flume
lone heartBOT
hardy flume
hello
i need help w this
answer is 3
got it to integral form
How do i find the antideriv of this??
limpid spade
power rule
hardy flume
can you show me? im trying to do that but keep getting the wrong answer
sand smelt
here you have an integration over x ig so you need to add dx at the end for the lineelement
limpid spade
what's integral of x^2
sand smelt
you can then simply apply the fundamental of diffenrtial and integral calculus
limpid spade
why
limpid spade
it's a constant
hardy flume
thats kinda where im lost
limpid spade
it's not the variable
limpid spade
what's integral of 1
hardy flume
x
limpid spade
so what's integral of c^2
lone heartBOT
@hardy flume Has your question been resolved?
fervent timber
how would I find the equation a 3d function with 2 independent variables?
fervent timber
I mean dependent
how would I find the equation a 3d function with 2 dependent variables?
specifically I want to graph sin(a+bi) where b is a constant
I'm trying to find an equation so I can see the graph in 3d
placid zinc
So b is not a dependent variable. Only a is?
fervent timber
the 2 dependent variables would be the real and imaginary part, I guess
b is a constant
a would be the independent variable I think
placid zinc
Or, haha whoops I mixed that up
fervent timber
yeah I could've made that more clear
placid zinc
sin(a + bi)
sin(a)cos(bi) + cos(a)sin(bi)
sin(a)cosh(b) + cos(a)sinh(b)i
fervent timber
yeah that's exactly what I have
placid zinc
,w graph sin(x + 2i)
ocean sealBOT
fervent timber
nice
placid zinc
And wolfram will give them to you
fervent timber
is it possible to have that in 3d?
like sin(z+2i) and the real part on the x-axis, imaginary part on the y-axis
so I can put it in here:
placid zinc
The problem is that you're only providing the information necessary to put a point on the x-y plane and y-z plane
placid zinc
Ye
fervent timber
how do I get this to work?
oh wait I probably need to set b
I set b=2 but it still doesn't work for some reason
I got it to work on desmos I think
am I supposed to be getting this?
placid zinc
I have no idea what you're supposed to be getting, what we're doing is random af
fervent timber
lol
placid zinc
Looks cool though
buoyant schooner
I need help with basic trigonometry
lone heartBOT
I need help with basic trigonometry
tacit arch
buoyant schooner
How do I do this
I'm so confused
It's super basic but I don't know how to solve it at all
safe needle
How do I do this
Supplementary angles and triangle angle sum
buoyant schooner
Supplementary angles and triangle angle sum
That's what this is called?
worn fox
supplementary angles on a line yeah
buoyant schooner
supplementary angles on a line yeah
Dumb question but there a calculator that can do this
buoyant schooner
I'm not sure
worn fox
they add up to 180, do you remember that?
buoyant schooner
I do
buoyant schooner
I know that
worn fox
so look at 3, we need the sum of those angles to add up to 180
so can you make an equation involving x?
buoyant schooner
180 is the most it can go and the two angles always make 180 in total
No honestly everything I know about math I forget
I need to solve the equation but how exactly
worn fox
we need to make an equation first
buoyant schooner
Where do we start
worn fox
we need angle_1 + angle_2 = 180 right?
buoyant schooner
Oh so add the two
worn fox
yep!
buoyant schooner
I can add them but the answer is going to be 180 which I already know though
worn fox
but we need to find x
so we make the equation by adding them and setting them equal to 180, and then we solve for x
buoyant schooner
How do I write the equation
worn fox
we need angle_1 + angle_2 = 180 right?
take this and replace with the angles given
worn fox
go on
worn fox
,w solve x-2+5x+2=180
ocean sealBOT
worn fox
yes
buoyant schooner
I really appreciate you
Do I do the same thing with the rest?
The other ones are a bit different though
worn fox
I really appreciate you
you're welcome!
the other ones are similar but you have to use the fact that angles in a triangle add to 180 aswell
rustic trout
can someone let me know how he got b in terms of a?
lone heartBOT
can someone let me know how he got b in terms of a?
merry depot
quadratic formula
rustic trout
quadratic formula
can you demonstrate how?
i don't see how we would manage b terms to = 0
merry depot
get it equal to 0, you get $b^2 + b -(a^2+1)=0$. Letting $b$ be your variable, you have coefficients $A=1$, $B=1$, and $C=-(a^2+1)$
ocean sealBOT
Zybikron
merry depot
plug those into $b = \frac{-B\pm \sqrt{B^2-4AC}}{2A}$
ocean sealBOT
Zybikron
cunning comet
can someone show me step by step on how to find the roots for y=10x - x^2
ocean sealBOT
iCaird
cunning comet
yes
worn fox
what does it look like if we do that?
cunning comet
x(10-x)=0 ?
cunning comet
i really dont know what to do after this part
worn fox
do you understand that is two numbers times to zero, then either one or the other is zero?
i.e. $ if ab=0$, then $a =0$ or $b=0$
ocean sealBOT
iCaird
cunning comet
i think
lone heartBOT
@cunning comet Has your question been resolved?
alpine sable
Hello I kinda need help with 2 math problems
lone heartBOT
Hello I kinda need help with 2 math problems
alpine sable
I have been looking at the for an hour without making any progress
I tried many different methods but all failed misserably
winter tangle
translate to english pls
alpine sable
There's nothing important being said
It just sais where you need to solve it
In this case x<1
They are 2 different exercises
winter tangle
There's nothing important being said
just translate so I can help
also show what you have already done
alpine sable
I've tried to ln both sides to get rid of the second one
Tried to make the 1st part of the first equation to one fraction
And then remove the ln again
Then I tried separating the ln in both problems
Ok I think I solved the second one
The first one still remains a mystery
The second one is x>-2
worn fox
,rotate
ocean sealBOT
lone heartBOT
@alpine sable Has your question been resolved?
tranquil pebble
lone heartBOT
thick talon
If you're doing f(g(x)), that means you have to plug in g(x) for each of the x values in f(x)
tranquil pebble
i got the answer but its grouped differently then the answer choices and thats why im confused
should i send answer choices
gray isle
show both your work and the available options
gray isle
wdym by grouped differently
swift shore
@tranquil pebble how is your answer any different from theirs
lone heartBOT
@tranquil pebble Has your question been resolved?
tranquil pebble
wdym by grouped differently
Look at the very first equation
G(f(x)) is right
But not f(g(x))
gray isle
how is your answer any different from theirs
on your page you seem to have written
f(g(x)) = 16x^2 - 12x - 1
which is exactly the same as what's in the option
@tranquil pebble
round chasm
dont know how it works
lone heartBOT
dont know how it works
round chasm
why (a-2)/5 and not just -2/5?
oak perch
5x^3+48x^2+100x+2-a=5(x-r_1)(x-r_2)(x-r_3)
proud locust
If I have a curve y = 4/(x^2), and I want to find the x value of a line that "bisects" the area under a restricted part of that curve (1 <= x <= 4), how would I do that
proud locust
"Bisect" meaning, if the bisecting line is x = a, the area under the curve to the left of a would be the same as the area under the curve to the right of a
I think I know how to do this in an abstract sense, I just don't know how to actually compute it
oak perch
Just solve difference of -4/x at value 4,a =difference of -4/x at a,1
swift shore
Just solve difference of -4/x at value 4,a =difference of -4/x at a,1
Wdym difference of at value
oak perch
I mean that
proud locust
what I have in mind is something to do with sequences
oak perch
Solve (-4/4)-(-4/a)=(-4/a)-(-4/1)
oak perch
Yeah
swift shore
@proud locust you know calculus right
swift shore
Just solve (integral from 1 to a of f(x)) = (integral from a to 4 of f(x)) for a
swift shore
A sequence? Wdym
proud locust
I was way overthinking it
proud locust
A sequence? Wdym
like, a sigma sum
swift shore
Oh
proud locust
Would it be possible to make a sigma notation sum with an unknown upper bound that would be the bisecting line's value
swift shore
Well what would you be summing exactly?
swift shore
Haha yeah that’s literally exactly what integration is
proud locust
that, when added together, would equal the area under the curve
proud locust
Haha yeah that’s literally exactly what integration is
oh right
swift shore
yesyesyesno
proud locust
I really don't like sums and limits
Back in the previous calc course when we were learning about more advanced limits I hated it so much and was like "okay I'm gonna slide through this and hope I'll never have to use these again"
well, shit
anyway thank you for pointing me in the right direction
drowsy flax
{(-6)(-6)} would the - sign carry over into the next step if both values are exactly the same like here
drowsy flax
{(-6)(-6)} would the - sign carry over into the next step if both values are exa...
<@&286206848099549185>
tacit arch
{(-6)(-6)} would the - sign carry over into the next step if both values are exa...
There's no question to answer. What is "next step"?
drowsy flax
There's no question to answer. What is "next step"?
.close
mossy burrow
lone heartBOT
mossy burrow
i need help with these 4 problems
mossy burrow
no idk how
carmine oar
sure
mossy burrow
i don’t know how to create equations
alpine sable
How much would the blend cost?
mossy burrow
17.70?
alpine sable
Thats per pound
carmine oar
first what are you looking for?
mossy burrow
how many pounds?
carmine oar
yes
carmine oar
first let the x be the weight of the kaapo bean
then total cost = cost of kaapo bean + cost of maui beans
lone heartBOT
@mossy burrow Has your question been resolved?
mossy burrow
first let the x be the weight of the kaapo bean
is it alright if we vc?
need help with these two
<@&286206848099549185>
gritty wave
I have 10 but not 9
gritty wave
set x as the amount of adults, 3x as the amount of girls
lone heartBOT
@mossy burrow Has your question been resolved?
simple turtle
i need help on 9
is this simple interest?
mossy burrow
is this simple interest?
i’m not sure
simple turtle
simple interest I = prt.
First, you want to say that x dollar = mutual fund. this means 40000-x dollars to other account.
@mossy burrow is it sounds good
mossy burrow
yes
mossy burrow
do you know how to set things up?
no thats what i struggle with
simple turtle
I will set it up like this:
Let interest 1 = .021 and interest 2 = .065
P1=x and P2=40000-x
interest earned from account 1 + interest earned from account 2 = 40000(.054) interest earned.
(40000-x)(.021)+.065x=400009(.054) Solve for x, it is 30000.
simple turtle
ok yes that makes sense!
you're welcome.
mossy burrow
I will set it up like this:
Let interest 1 = .021 and interest 2 = .065
P1=x and...
did u accidently put a 9?
simple turtle
did u accidently put a 9?
Yes, sorry. typo
simple turtle
ok thank u
Just want to mention one thing. I = PRT, the T=time cancels out because it is same length of time so you don't even have to consider T
mossy burrow
ohhh interesting
simple turtle
ohhh interesting
another typo, Let
interest 2 = .021
P2=40000-x
and interest 1 = .065
P1=x
I had interest numbered wrong to match the formula.
(40000-x)(.021) +.065x=40000(.054)
If you want to set it up this way, still it comes up with the same number. 10000 to one account and 30000 to another account.
(40000-x)(.065) +.021x=40000(.054)
mossy burrow
oh ok that makes sense too
mossy burrow
another typo, Let
interest 2 = .021
P2=40000-x
and interest 1 = .065
P1=x
...
i do have another problem
its easy
i just dont know how to set it up
nvm i got it
simple turtle
ok. just multiply to numbers. 32321(.157) Mark is nice.
simple turtle
nvm i got it
good
sand star
lone heartBOT
sand star
Just wondering am I on the right track?
lone heartBOT
@sand star Has your question been resolved?
alpine sable
lone heartBOT
alpine sable
how do i solve for this?
alpine sable
how do i solve for this?
as in how do you get
x = 0.5275*L
minor wedge
apply the quadratic formula where a=3, b=6L, c=-4*sqrL
alternatively, this can also be a quadratic equation in terms of L such that a=-4, b=6x, c=3sqrx
minor wedge
by sqrL i mean L squared
alpine sable
ohhhh
i tried doing that but i think i just didnt want to solve it in the end thinking there couldve been an easier method
ill try it again tho tyty
minor wedge
np
alpine sable
.close
mental scroll
What is a derivative in maths
lone heartBOT
What is a derivative in maths
oak perch
Depends on the subject
minor wedge
What is a derivative in maths
the derivative of a function is the rate of change of that function
it defines how fast or how slow the fucntion will move
oak perch
There are derivative of a chain complex, cocomplex, derivative in a operator algebra. You need to specify which subject you are talking about
oak perch
Partial derivative, given a f:R^n—>R, mapping (x_1,…,x_n) to f(x_1,…,x_n), the first order partial derivative of f in terms of x_j is the derivative of f of x_j while viewing all other variables as constants
So $\frac{\partial f}{\partial x_{j}}(x_{1},…,x_{n})=\lim_{y \to x_{j}}\frac{f(x_{1},…,y,…,x_{n})-f(x_{1},…,x_{j},…,x_{n})}{y-x_{j}}$
ocean sealBOT
Cogwheels of the mind
mental scroll
Is this a formula
oak perch
No
This is the definition of first order partial derivative of f in terms of x_j at point (x_1,…,x_n)
mental scroll
Didn't get
alpine sable
What is a derivative in maths
Describes how fast a function is changing at a particular time
if we have a car and the distance covered by that care by time t is t^2 the velocity of that car at t is the derivative of t^2
mental scroll
Didn't get
mental scroll
if we have a car and the distance covered by that care by time t is t^2 the velo...
How will you express In formula
lone heartBOT
@mental scroll Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
wet beacon
Guys I have a question
lone heartBOT
Guys I have a question
wet beacon
Is that ALL linear equations except the denominator has unknown is ALWAYS a straight line?
also no turning points
I'm a grade 8 student, just learnt simultaneous equations
worn fox
Any equation that looks like y =ax + c represents a straight line
limpid spade
YES
worn fox
Is that what you're asking?
wet beacon
yes thanks
I watched videos like y=mx+c and y=mx+b
what about more unknowns
like y=ax+bz+c
limpid spade
multivariable is not grade 8
wet beacon
for example, is y=3x+5z+18 a straight line
limpid spade
your graph would be 3dimensional
worn fox
It's not multivariable calc
wet beacon
multivariable is not grade 8
but they already taught us...
limpid spade
wghattt
worn fox
for example, is y=3x+5z+18 a straight line
This would give you a plane in 3D
lone heartBOT
Given a quadrilateral like in the figure
alpine sable
Find the area
Ur asked to find the formula of the arra
Any measurements from the diagram?
lone heartBOT
@thick lynx Has your question been resolved?
jagged flume
Hey
jagged flume
The functions are known to intersect at the point x=1 and both have the same slope at x = -0.25. Find A and B
So I found A which is 1, how do I find B?
sudden hinge
picture is cut off
jagged flume
Yes, because it's in a different language. I wrote all the details here
jagged flume
I'll tell you what I did so far
I found g'(x) and f'(x) which are-
g'(x) = 2x
f'(x) = 6x+A
I equaled between them and replaced X with -0.25 and I found that A = 1
After I did that, what do I have to do in order to find B?
worn fox
Use the fact that they intersect at x=1
tame hound
- In a class of 24 students, half of the boys have a bicycle. How many girls in the class have a bicycle?
(1) There are as many girls as boys in the class. 14 students do not have a bicycle.
(2) Of those who do not have a bicycle, the girls are 2 more than the boys. Of the girls, those who do not have a bicycle 4 are more than those who have a bicycle.
Can we solve the task with information (1) and (2) separately, or together?
sudden hinge
Can't you solve it already with just (1)?
alpine sable
Can't you solve it already with just (1)?
That's all he even asked ig
If he can do it with only 1
Or if both are needed
I don't think we can solve it only with 1 tho
tame hound
It's doable with (1) right? But I'm interested in knowing what methods y'all would use to solve it as fast as possible
sudden hinge
24 students, 12 boys & 12 girls. half of the boys have a bicycle => 6 bicycles. 14 have no bicycle, so 10 have bicycles
tame hound
In a multiple-choice question
sudden hinge
means 4 girls need to have bicycles
tame hound
24 students, 12 boys & 12 girls. half of the boys have a bicycle => 6 bicycles. ...
Do we need variables?
alpine sable
Oh right we can do it with (1)
sudden hinge
you can solve it with variables too
tame hound
What variables would you use for (1)?
x = 24 students?
or x for boys (with a bicycle and without)?
alpine sable
means 4 girls need to have bicycles
Eh I think it will be 14-6=8
sudden hinge
so 8 + 6 = 14 bicycles. but the problem states that 14 do not have bicycles
tame hound
yes so 10 students have a bicycle
in (1)
there is also as many girls as boys in the class in (1)
so right away, 12 girls + 12 boys
and 6 boys own a bicycle, 6 does not
alpine sable
so 8 + 6 = 14 bicycles. but the problem states that 14 do not have bicycles
Oh man I read the opposite srry
tame hound
10 students have a bicycle, so 10 students with a bicycle - 6 boys with a bicycle = 4 girls with a bicycle
that's from (1)
what about (2)?
sudden hinge
2 is more interesting
tame hound
someone posted this (in swedish), but i'm not sure if it's for (2) or (1)
seems like it's for (2), and it's solvable this way
so, x = boys with a bicycle, and x = boys without a bicycle, do we add them together?
sudden hinge
So they partition it into all 4 possible groups first
- boys with bicycle, boys without bicycle
- girls with bicycle, girls without bicycle
Adding them all together gives us 4x = 24 or x = 6.
Then because you're written everything in terms of only 1 variable, you just select the right combination of row+column to pick out the info you want
tame hound
Then because you're written everything in terms of only 1 variable, you just sel...
And that one variable being amount of students with a bicycle? Or is it amount of boys with a bicycle = amount of boys without a bicycle?
real mason
hi together, i currently work on "lectures on the poisson process" (written by Last and Penrose). I struggle with an exercise in the book, more explicit exercise 2.3 which i screenshoted down here. My intention was to show that this infinite sum of point processes is measurable. but i dont know how to progress on this. the hint doesnt help me at all tbh.
real mason
so i started to do this by checking if {m(B)=k}={\sum_n=1}^\infty m_n(B)=k} is measurable. but i really dont know how to get to a solution.
lone heartBOT
@real mason Has your question been resolved?
real mason
<@&286206848099549185>
lone heartBOT
@real mason Has your question been resolved?
lone heartBOT
@real mason Has your question been resolved?
steep lion
lone heartBOT
steep lion
What does the ko stand for here? It’s a lil formula for the double integral over an area, for a continuous f: A -> R
worn fox
is there more context here? could be anything as is
bitter vault
What does the **ko** stand for here? It’s a lil formula for the double integral ...
Maybe a misprint
steep lion
Yeah, just checked with the professor, it’s a misprint
spiral glen
anyone's able to explain solving this kind of stuff?
lone heartBOT
anyone's able to explain solving this kind of stuff?
spiral glen
i understand that using a unit circle is needed, also i do understand how to use this unit circle, but i don't really get solving this kind of equations in general
worn fox
If we let $y = 4x + \frac{\pi}{3}$, we are looking for solutions to $sin(y) = -\frac{\sqrt{3}}{2}$
ocean sealBOT
iCaird
worn fox
does that makes sense?
spiral glen
yes it is
worn fox
and so you know how to use the unit circle to solve the new equation for y?
alpine sable
anyone's able to explain solving this kind of stuff?
do you know the trig table?
spiral glen
ah, so
sin(y)=4p/3 & sin(y) = 5p/3
and i need to solve a pair of equations which are
4x+p/3=5p/3 + 2pk & 4x+p3=4p/3 + 2pk?
lone heartBOT
@spiral glen Has your question been resolved?
viscid rose
viscid rose
i was having a hard time with the first two
quasi scarab
what was the problem
south flicker
can someone pls help me with this? id really appreaciate it
quasi scarab
@south flicker#❓how-to-get-help
lone heartBOT
@viscid rose Has your question been resolved?
median mauve
I have no idea completely, can somebody give me some idea.
lone heartBOT
I have no idea completely, can somebody give me some idea.
@median mauve Has your question been resolved?
tacit arch
notice that (x+1/x)(y+1/y) = a
median mauve
notice that (x+1/x)(y+1/y) = a
hmm why
median mauve
(x+1/x)(y+1/y) = a
median mauve
:(
median mauve
yea :(
lone heartBOT
@median mauve Has your question been resolved?
lone heartBOT
@median mauve Has your question been resolved?
drifting hull
@median mauve if you choose a=100 and b=7, then you get $x^2+y^2=\frac{10049}{200}$. This should help you to find a nice factoring
ocean sealBOT
Alexander42
median mauve
<@782087086416461855> if you choose a=100 and b=7, then you get $x^2+y^2=\frac{1...
I am little bit confuse
drifting hull
as it is pretty much impossible to get the exact values of x and y, one needs a different approach. The idea is that one can express x^2+y^2 as a term in a and b.
The question is, which expression in a and b is the right one. For that one needs some guessing. One can look at an example, eg a=100 and b=7. For this case (with help of wolfram alpha), one can caluculate the solutions of the equations and then calculate $x^2+y^2$ for these solutions. You get $x^2+y^2=\frac{10049}{200}$. So if we plug in a=100 and b=7 in this term, we get $\frac{10049}{200}$. Now one has to guess a nice-looking term that yields $\frac{10049}{200}$ if you plug in a=100 and b=7.
ocean sealBOT
Alexander42
median mauve
The question is, which expression in a and b is the right one. For that one need...
How this proof the sum $x^2 + y^2$ is real for any real a and b.
ocean sealBOT
LittleMouse
drifting hull
the idea is if eg $x^2+y^2=(x^2+x^2+xy+\frac{1}{xy})/(x^4+y^4+x^2y^2-\frac{1}{x^2y^2}-2)$, then one can use the two equations we have, which then yields $x^2+y^2=\frac{a}{b^2}$ and is therefore a real number
ocean sealBOT
Alexander42
drifting hull
the idea is to do something like this
Notice that the first equality sign is incorrect
drifting hull
i will go to bed, now. I suggest you close this channel and open a new one with the new question...